US7801253B1 - Nonlinear post-processors for channels with signal-dependent noise - Google Patents
Nonlinear post-processors for channels with signal-dependent noise Download PDFInfo
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- US7801253B1 US7801253B1 US11/410,688 US41068806A US7801253B1 US 7801253 B1 US7801253 B1 US 7801253B1 US 41068806 A US41068806 A US 41068806A US 7801253 B1 US7801253 B1 US 7801253B1
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- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
- G11B20/10—Digital recording or reproducing
- G11B20/10009—Improvement or modification of read or write signals
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- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
- G11B20/10—Digital recording or reproducing
- G11B20/10009—Improvement or modification of read or write signals
- G11B20/10268—Improvement or modification of read or write signals bit detection or demodulation methods
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- G—PHYSICS
- G11—INFORMATION STORAGE
- G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
- G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
- G11B20/10—Digital recording or reproducing
- G11B20/10009—Improvement or modification of read or write signals
- G11B20/10305—Improvement or modification of read or write signals signal quality assessment
- G11B20/10398—Improvement or modification of read or write signals signal quality assessment jitter, timing deviations or phase and frequency errors
- G11B20/10407—Improvement or modification of read or write signals signal quality assessment jitter, timing deviations or phase and frequency errors by verifying the timing of signal transitions, e.g. rising or falling edges, or by analysing signal slopes
Definitions
- This invention relates generally to apparatus and methods for decoding communication signals, and, more particularly, to decoding communication signals containing signal-dependent noise.
- perpendicular recording In order to increase the areal densities of magnetic media even further, many media manufacturers are using perpendicular recording. Unlike traditional longitudinal recording, where the magnetization is lying in the plane of the magnetic medium, with perpendicular recording the media grains are oriented in the depth of the medium with their magnetization pointing either up or down, perpendicular to the plane of the disc. Using perpendicular recording, manufacturers have exceeded magnetic recording densities of 100 Gbits per square inch, and densities of 1 Terabit per square inch are feasible.
- the post-processor may be used to output the final decision of a sub-optimal detector, such as a linear or non-linear Viterbi detector.
- the post-processor may be used to correct or reduce decision errors due to signal-dependent and/or additive white noise.
- the post processor may receive a set of preliminary decisions from a sub-optimal detector along with a sampled data signal (before or after equalization). The post-processor may then compute the transition jitter associated with each preliminary decision in the set and assign a cost metric to each decision. The post-processor may output the decision with the lowest cost metric as the final decision of the detector.
- the post-processor may compute the transition jitter and white noise of the channel so that the overall noise is minimized.
- other types of noise such as pulse width noise, are incorporated into the metric calculations.
- a sub-optimal detector such as a linear or non-linear Viterbi detector, may output a set of candidate decisions to the post-processor, which selects the decision with the overall lowest cost.
- detector means may compute a set of preliminary detector decisions associated with received signal samples.
- Post-processing means may be used to estimate at least one form of signal-dependent noise associated with each preliminary detector decision and assign a cost metric to each decision based on the noise estimate.
- Output means may select the decision with the lowest overall cost metric as the final detector decision.
- a receiver contains signal processing means that may filter a communication signal and generate an input signal. Detector means may then detect the data in the input signal by generating a set of preliminary detector paths corresponding to the data in the input signal. Post-processing means may receive the input signal and the set of preliminary detector paths and estimate at least one form of signal-dependent noise for each path in the set. The post-processing means may also assign a cost metric to each path in the set based on the noise estimate and select the final detector decision.
- a receiver includes a computer program running on a processor for reading a data signal from a recording channel.
- the program may include program logic for filtering a communication signal and generating an input signal therefrom.
- the program logic may then detect data in the input signal by generating a set of preliminary detector paths corresponding to the data in the input signal.
- the program logic may estimate at least one form of signal dependent noise for each path in the set and assign a cost metric to each path based on the noise estimate.
- One of the preliminary detector paths in the set may be selected by the program logic based on the cost metrics.
- a computer program running on a processor for correcting the output of a sub-optimal detector.
- the program may include program logic to generate a set of preliminary detector decisions for received signal samples.
- the program logic may then estimate at least one form of signal dependent noise associated with each preliminary decision in the set and assign a cost metric to each decision based on the noise estimate.
- the program logic may then output the decision with the lowest cost metric as the final detector output.
- the post-processor of the present invention is part of a receiver including signal processing circuitry to filter a communications signal and generate an input signal therefrom.
- a signal detector may receive the input signal and generate a set of preliminary detector decisions.
- a post-processor may then compute the transition jitter associated with each preliminary decision in the set and assign a cost metric to each decision.
- the post-processor may then output the decision with the lowest noise cost as the final decision of the detector.
- FIG. 1 is a simplified block diagram of an illustrative noise model for a recording channel in accordance with one embodiment of the invention
- FIG. 2 is an illustrative linearized noise model for small transition jitter noise in accordance with one embodiment of the invention
- FIG. 3 is a simplified block diagram of illustrative detection apparatus in accordance with one embodiment of the invention.
- FIG. 4 is a more detailed, yet still simplified, block diagram of the illustrative post-processor circuitry of FIG. 3 in accordance with one embodiment of the invention
- FIG. 5 is a simplified block diagram of an illustrative iterative metric computation block of FIG. 4 in accordance with one embodiment of the invention
- FIG. 6 is an alternative embodiment of the illustrative detection apparatus of FIG. 3 ;
- FIG. 7 is a flowchart showing an illustrative process for detecting a signal in accordance with one embodiment of the invention.
- FIG. 8 is a flowchart showing an illustrative process for selecting a final decision from a set of preliminary decisions in accordance with one embodiment of the invention.
- FIG. 9A is a block diagram of an exemplary hard disk drive that can employ the disclosed technology.
- FIG. 9B is a block diagram of an exemplary digital versatile disc that can employ the disclosed technology.
- FIG. 9C is a block diagram of an exemplary high definition television that can employ the disclosed technology.
- FIG. 9D is a block diagram of an exemplary cell phone that can employ the disclosed technology.
- FIG. 9E is a block diagram of an exemplary set top box that can employ the disclosed technology.
- FIG. 9F is a block diagram of an exemplary media player that can employ the disclosed technology.
- Embodiments of the present invention relate to apparatus and methods for post-processing data channels, particularly magnetic recording channels.
- the present invention can be used to post-process any communication channel in which a sub-optimal detector is used, such as optical and magneto-optical channels.
- FIG. 1 depicts a simplified block diagram of illustrative noise model 100 for a typical recording channel.
- User data (perhaps selected from the set ⁇ +1, ⁇ 1 ⁇ ) may be converted to the form of signed NRZI by block 102 resulting in data signal b k .
- This signal may indicate whether there is a transition in the data signal and also the polarity of the transition, if it exists.
- Noise in the form of transition jitter may then be added to the signal at block 104 , where the transition jitter, ⁇ k , may be modeled by a noise process N j having a mean of 0 and a standard deviation of ⁇ j .
- This signal may then be applied to the channel step response s(t) at block 106 .
- additive white noise w k
- the additive white noise may be modeled by a noise process N w with a mean of 0 and a standard deviation of ⁇ w .
- the resulting signal of noise model 100 may be the convolution of data signal b k and the channel step response plus some white noise:
- y ⁇ ( t ) ⁇ k ⁇ ⁇ b k ⁇ s ⁇ ( t - kT s - ⁇ k ) + n w ⁇ ( t ) ( EQ ⁇ ⁇ 1 )
- FIG. 2 shows illustrative linearized noise model 200 for small transition jitter noise.
- the example of FIG. 2 uses a first order Taylor approximation of the transition jitter, i.e.: s ( t ⁇ kT s ⁇ k ) ⁇ s ( t ⁇ kT s ) ⁇ k s ′( t )
- t kT s (EQ 2)
- the user data, u k may be passed through block 202 . Since transition jitter is only present when there is a transition in the user data (e.g., from +1 to ⁇ 1 or from ⁇ 1 to +1), multiplication unit M 1 may be used to model the transition jitter.
- the output of multiplier 206 may be applied to differentiated step response 208 , resulting in a value of the transition jitter. This value may be added to dibit response 204 (the response of two adjacent transitions in the user data) and an additive white noise process by adder 210 .
- FIG. 2 uses a first-order Taylor approximation of the transition jitter. As previously discussed, this approximation is not an optimal approximation for noise processes with a high variance. However, the second order approximation for the transition jitter is closer to optimal, but computationally expensive. Therefore, to reduce the complexity of the post-processor, some embodiments of the invention compute a finite number of second order approximations corresponding to a finite number of preliminary detector decisions, or survival paths, b k .
- the second order approximation for the transition jitter may be represented by:
- the signal output y k corresponding to survival path b k may be represented as:
- the noise attributed to transition jitter, ⁇ k can be estimated from time K 2 ⁇ min (M 1 , N 1 ) to time K 1 ⁇ min(M 2 , N 2 ).
- the white noise, w k can also be estimated from time K 1 to K 2 such that overall noise is minimized. This is equivalent to the optimization problem of minimizing the decision metric, ⁇ 2 , where
- the first term in EQ 5 may represent the cost associated with one or more sources of signal-dependent noise, such as transition jitter.
- the second term in EQ 5 may represent the cost metric associated with additive white noise.
- EQ 5 has a unique solution and can be readily computed by well-known optimization algorithms. For example, an iterative method of solving EQ 5 is depicted in algorithm 500 of FIG.
- a separate decision metric ⁇ 2 may be computed for each preliminary decision, b n .
- the number of the preliminary decisions considered using this algorithm may be finite. Therefore, the complexity of the system as a whole may be greatly reduced.
- a look-up table may be used instead of approximating the transition jitter, ⁇ k , and the white noise, w k . This may help reduce computation. Given the signal output y k and the preliminary detector decision b k , the noise values ⁇ k and w k (and even the decision metric ⁇ 2 ) may be obtained from the look-up table. Additionally or alternatively, a look-up table may also be used to evaluate EQ. 4. So, for example, given noise values ⁇ k and w k , the expected signal output corresponding to survival path b k may be obtained from a table and then compared to the actual received signal.
- FIG. 3 shows illustrative detection apparatus 300 in accordance with one embodiment of the invention.
- An analog read signal may be read from channel 302 by front end 304 .
- channel 302 may be a magnetic recording channel and front end 304 may include analog filters, gain control, and a timing recovery system.
- Signal samples y may be equalized by equalizer 306 before entering detector block 308 .
- Equalizer 306 may be, for example, a FIR equalizer.
- Detector block 308 may include any suitable sub-optimal detector.
- detector block 308 includes a Viterbi or Viterbi-like detector; however a PRML detector, a tree/trellis detector, a decision feedback detector, or a hybrid detector, for example, may be used in other embodiments.
- Detector block 308 may create a set of preliminary signal decisions of the channel data and provide these decisions to post-processor block 310 .
- Signal samples y may also be routed to post-processor block 310 .
- Post-processor block 310 may receive the signal samples and the set of preliminary decisions and compute a metric for each preliminary decision. This metric may be computed by minimizing the decision metric of EQ 5 using any known method. For example, algorithm 500 ( FIG. 5 ) may be used to calculate decision metrics in some embodiments. Post-processor block 310 may compare all the computed decision metrics and output the decision associated with the metric of the lowest cost. This decision may then be output as the final decision of detector block 308 .
- detector 308 may include post-processor 310 in a single, integrated device.
- detector 306 or post-processor 310 may include the equalization functionality of equalizer block 306 .
- equalization may not be used and equalizer block 306 may be removed from detection apparatus 300 entirely.
- FIG. 4 shows the illustrative post-processor block of FIG. 3 in more detail.
- Post-processor 400 may receive signal samples y and one or more preliminary signal decisions b n .
- Computation blocks 402 , 404 , and 406 may compute the decision metric ⁇ 2 for each preliminary decision received from detector 308 ( FIG. 3 ).
- the resultant decision metric of each computation block may be a representation of the total cost (e.g., an estimation of the signal-dependent and additive white noises) associated with the decision.
- Block 408 may select the smallest decision metric ⁇ 2 received from computation blocks 402 , 404 , and 406 .
- Block 408 may provide the minimum decision metric to multiplexer 410 , which selects and outputs the appropriate decision as the detector's final decision.
- computation blocks 402 , 404 , 406 may be synchronous or asynchronous blocks.
- post-processor 400 may be performed in software.
- a program running on a processor may include program logic.
- the program logic may compute the decision metric ⁇ 2 associated with each received preliminary decision b n and select the decision with the smallest metric.
- the program logic may then output the decision with the smallest metric from post-processor 400 .
- a combination of hardware and software may be used to implement the functionality of post-processor 400 in other embodiments.
- FIG. 5 shows an illustrative algorithm 500 that may be used to calculate decision metrics in accordance with one embodiment of the invention.
- One or more of computation blocks 402 , 404 , and 406 of FIG. 4 may use algorithm 500 .
- Algorithm 500 may be an iterative algorithm designed to stop once one or more stop conditions have been met.
- initial values of the transition jitter, ⁇ k , and the white noise, w k may be selected to satisfy EQ 4.
- the value of the decision metric, ⁇ 2 may be computed by block 504 using the current values of ⁇ k and w k . Stopping block 506 may determine if one or more user or system-defined stop conditions have been met.
- the current value of ⁇ 2 may be output of the computation block. If stopping block 506 determines that one or more stop conditions have not been met, new values of ⁇ k and w k may be selected based on, for example, the current or previous value of ⁇ 2 , its gradient, or any other suitable criteria.
- the stopping criteria used by stopping block 506 may depend on a number of system or user-defined criteria, including, for example, the incoming data rate of the recording channel, the number of decisions to process, overall system performance, and desired metric accuracy. Often times, the performance benefit of stopping the iterative calculation early outweighs the negligible increase in accuracy of the iterative metric. Thus, in some embodiments the stopping criteria is based on the rate of change of ⁇ 2 . In other embodiments, a user-programmable number of iterations is read by stopping block 506 . Algorithm 500 may then automatically stop after the user-programmed number of iterations has been reached.
- FIG. 6 shows another illustrative embodiment of the detection apparatus in accordance with the invention.
- detection apparatus 600 may include channel 602 , front end 604 , equalizer 606 , detector 608 , and post-processor 610 .
- post-processor 610 may operate on the output of equalizer 606 rather than the unequalized output of front end 604 . If post-processor 610 operates on the output of equalizer 606 , the noise models used in EQS 4 and 5 may be slightly different to account for the equalized samples. Otherwise, the operation of detection apparatus 600 may be similar or the same as the operation of detection apparatus 300 ( FIG. 3 ).
- FIG. 7 shows illustrative process 700 for correcting the preliminary decision provided by a suboptimal detector.
- the signal is read from the channel.
- front end 304 FIG. 3
- 604 FIG. 6
- the data may be equalized.
- the read signal may be passed through equalizer 306 ( FIG. 3 ) or 606 ( FIG. 6 ).
- the detector may generate a list of preliminary decisions of the signal received at step 702 .
- the post-processor may then select a final decision from the list of preliminary decisions provided by the detector at step 708 . Step 708 is shown in more detail in FIG. 8 .
- the post-processor may output the final decision at step 710 before the illustrative process begins again.
- FIG. 8 shows illustrative process 800 for computing cost metrics associated with the set of preliminary detector decisions and selecting the final decision of a sub-optimal detector.
- the post-processor may received one or more preliminary detector decisions from a sub-optimal detector.
- the detector need only provide a reliable list of decisions (i.e., the probability of the true decision being in the list is high). This greatly reduces the complexity of the system because the post-processor may only compute the metrics associated with a small, finite number of potential decisions (as opposed to, for example, the entire tree or trellis).
- the first metric is computed for decision b n .
- the post-processor may select the smallest metric at step 808 and output the decision associated with the smallest metric at step 810 .
- the post-processor architecture described above may correct a suboptimal detector's output my modeling transition jitter and white noise
- other types of noise may be detected as well.
- a pulse width noise model may be incorporated into the noise calculations.
- the aforementioned post-processing architecture may select the detector decision with the lowest overall weighted sum of the transition jitter, the pulse width noise, and the white noise (or any other desired set of noises) associated with the input signal.
- FIGS. 9A-9F various exemplary implementations of the present invention are shown.
- the present invention can be implemented in a hard disk drive 900 .
- the present invention may implement either or both signal processing and/or control circuits, which are generally identified in FIG. 9A at 902 .
- the signal processing and/or control circuit 902 and/or other circuits (not shown) in the HDD 900 may process data, perform coding and/or encryption, perform calculations, and/or format data that is output to and/or received from a magnetic storage medium 906 .
- the HDD 900 may communicate with a host device (not shown) such as a computer, mobile computing devices such as personal digital assistants, cellular phones, media or MP3 players and the like, and/or other devices via one or more wired or wireless communication links 908 .
- the HDD 900 may be connected to memory 909 such as random access memory (RAM), low latency nonvolatile memory such as flash memory, read only memory (ROM) and/or other suitable electronic data storage.
- RAM random access memory
- ROM read only memory
- the present invention can be implemented in a digital versatile disc (DVD) drive 910 .
- the present invention may implement either or both signal processing and/or control circuits, which are generally identified in FIG. 9B at 912 , and/or mass data storage of the DVD drive 910 .
- the signal processing and/or control circuit 912 and/or other circuits (not shown) in the DVD 910 may process data, perform coding and/or encryption, perform calculations, and/or format data that is read from and/or data written to an optical storage medium 916 .
- the signal processing and/or control circuit 912 and/or other circuits (not shown) in the DVD 910 can also perform other functions such as encoding and/or decoding and/or any other signal processing functions associated with a DVD drive.
- the DVD drive 910 may communicate with an output device (not shown) such as a computer, television or other device via one or more wired or wireless communication links 917 .
- the DVD 910 may communicate with mass data storage 918 that stores data in a nonvolatile manner.
- the mass data storage 918 may include a hard disk drive (HDD).
- the HDD may have the configuration shown in FIG. 9A .
- the HDD may be a mini HDD that includes one or more platters having a diameter that is smaller than approximately 1.8′′.
- the DVD 910 may be connected to memory 919 such as RAM, ROM, low latency nonvolatile memory such as flash memory and/or other suitable electronic data storage.
- the present invention can be implemented in a high definition television (HDTV) 920 .
- the present invention may implement either or both signal processing and/or control circuits, which are generally identified in FIG. 9C at 922 , a WLAN interface and/or mass data storage of the HDTV 920 .
- the HDTV 920 receives HDTV input signals in either a wired or wireless format and generates HDTV output signals for a display 926 .
- signal processing circuit and/or control circuit 922 and/or other circuits (not shown) of the HDTV 920 may process data, perform coding and/or encryption, perform calculations, format data and/or perform any other type of HDTV processing that may be required.
- the HDTV 920 may communicate with mass data storage 927 that stores data in a nonvolatile manner such as optical and/or magnetic storage devices. At least one HDD may have the configuration shown in FIG. 9A and/or at least one DVD may have the configuration shown in FIG. 9 B. The HDD may be a mini HDD that includes one or more platters having a diameter that is smaller than approximately 1.8′′.
- the HDTV 920 may be connected to memory 928 such as RAM, ROM, low latency nonvolatile memory such as flash memory and/or other suitable electronic data storage.
- the HDTV 920 also may support connections with a WLAN via a WLAN network interface 929 .
- the present invention can be implemented in a cellular phone 930 that may include a cellular antenna 931 .
- the present invention may implement either or both signal processing and/or control circuits, which are generally identified in FIG. 9D at 932 , a WLAN interface and/or mass data storage of the cellular phone 930 .
- the cellular phone 930 includes a microphone 936 , an audio output 938 such as a speaker and/or audio output jack, a display 940 and/or an input device 942 such as a keypad, pointing device, voice actuation and/or other input device.
- the signal processing and/or control circuits 932 and/or other circuits (not shown) in the cellular phone 930 may process data, perform coding and/or encryption, perform calculations, format data and/or perform other cellular phone functions.
- the cellular phone 930 may communicate with mass data storage 944 that stores data in a nonvolatile manner such as optical and/or magnetic storage devices for example hard disk drives HDD and/or DVDs. At least one HDD may have the configuration shown in FIG. 9A and/or at least one DVD may have the configuration shown in FIG. 9B .
- the HDD may be a mini HDD that includes one or more platters having a diameter that is smaller than approximately 1.8′′.
- the cellular phone 930 may be connected to memory 946 such as RAM, ROM, low latency nonvolatile memory such as flash memory and/or other suitable electronic data storage.
- the cellular phone 930 also may support connections with a WLAN via a WLAN network interface 948 .
- the present invention can be implemented in a set top box 950 .
- the present invention may implement either or both signal processing and/or control circuits, which are generally identified in FIG. 9E at 954 , a WLAN interface and/or mass data storage of the set top box 950 .
- the set top box 950 receives signals from a source such as a broadband source and outputs standard and/or high definition audio/video signals suitable for a display 958 such as a television and/or monitor and/or other video and/or audio output devices.
- the signal processing and/or control circuits 954 and/or other circuits (not shown) of the set top box 950 may process data, perform coding and/or encryption, perform calculations, format data and/or perform any other set top box function.
- the set top box 950 may communicate with mass data storage 960 that stores data in a nonvolatile manner.
- the mass data storage 960 may include optical and/or magnetic storage devices for example hard disk drives HDD and/or DVDs. At least one HDD may have the configuration shown in FIG. 9A and/or at least one DVD may have the configuration shown in FIG. 9B .
- the HDD may be a mini HDD that includes one or more platters having a diameter that is smaller than approximately 1.8′′.
- the set top box 950 may be connected to memory 964 such as RAM, ROM, low latency nonvolatile memory such as flash memory and/or other suitable electronic data storage.
- the set top box 950 also may support connections with a WLAN via a WLAN network interface 966 .
- the present invention can be implemented in a media player 970 .
- the present invention may implement either or both signal processing and/or control circuits, which are generally identified in FIG. 9F at 974 , a WLAN interface and/or mass data storage of the media player 970 .
- the media player 970 includes a display 977 and/or a user input 1108 such as a keypad, touchpad and the like.
- the media player 970 may employ a graphical user interface (GUI) that typically employs menus, drop down menus, icons and/or a point-and-click interface via the display 977 and/or user input 978 .
- GUI graphical user interface
- the media player 970 further includes an audio output 979 such as a speaker and/or audio output jack.
- the signal processing and/or control circuits 974 and/or other circuits (not shown) of the media player 970 may process data, perform coding and/or encryption, perform calculations, format data and/or perform any other media player function.
- the media player 970 may communicate with mass data storage 980 that stores data such as compressed audio and/or video content in a nonvolatile manner.
- the compressed audio files include files that are compliant with MP3 format or other suitable compressed audio and/or video formats.
- the mass data storage may include optical and/or magnetic storage devices for example hard disk drives HDD and/or DVDs. At least one HDD may have the configuration shown in FIG. 9A and/or at least one DVD may have the configuration shown in FIG. 9B .
- the HDD may be a mini HDD that includes one or more platters having a diameter that is smaller than approximately 1.8′′.
- the media player 970 may be connected to memory 974 such as RAM, ROM, low latency nonvolatile memory such as flash memory and/or other suitable electronic data storage.
- the media player 970 also may support connections with a WLAN via a WLAN network interface 986 . Still other implementations in addition to those described above are contemplated.
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Abstract
Description
s(t−kT s−Δk)≈s(t−kT s)−Δk s′(t)|t=kT
Similar to
where M1<M2 and N1<N2. By sampling the signal output yk (either before or after equalization), the noise attributed to transition jitter, Δk, can be estimated from time K2−min (M1, N1) to time K1−min(M2, N2). In addition, the white noise, wk, can also be estimated from time K1 to K2 such that overall noise is minimized. This is equivalent to the optimization problem of minimizing the decision metric, ε2, where
while still satisfying EQ 4. The first term in EQ 5 may represent the cost associated with one or more sources of signal-dependent noise, such as transition jitter. The second term in EQ 5 may represent the cost metric associated with additive white noise. EQ 5 has a unique solution and can be readily computed by well-known optimization algorithms. For example, an iterative method of solving EQ 5 is depicted in
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US8947812B1 (en) | 2014-03-27 | 2015-02-03 | Western Digital Technologies, Inc. | Data storage device comprising equalizer filter and inter-track interference filter |
US9183877B1 (en) | 2015-03-20 | 2015-11-10 | Western Digital Technologies, Inc. | Data storage device comprising two-dimensional data dependent noise whitening filters for two-dimensional recording |
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